OFFSET
1,1
COMMENTS
If k is a palindrome (A002113), then 100*k is a term. If k is a term, then 100*k is a term. - Chai Wah Wu, Mar 31 2018
From Bernard Schott, Jan 02-10 2019: (Start)
There are six different families of integers in this sequence.
1) If k and rev(k) do not have the same number of digits:
All these integers are in A322835 where the first four families are explained and detailed.
Family 1: A002113(j) * 100^k
Family 2: A035090(j) * 100^k
Family 3: A082994(j) * 100^k
Family 4: A323061(j) * 10^(2k+1)
2) If k and rev(k) have the same number of digits.
All these integers are in A062917.
Family 5: Non-palindromic squares whose reverse is also square. These integers are in A035090.
Family 6: Non-palindromic numbers k, such that k * rev(k) is a square, with k and rev(k) not both square. These integers are in A082994.
3) Relationships between these different sequences.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Reinhard Zumkeller)
EXAMPLE
a(2)=144: rev(144)=441, 144*441=(12^2)*(21^2)=(12*21)^2 and 144<>12*21=252.
From Bernard Schott, Jan 02 2019: (Start)
Example for family 1: 200 * 2 = 400 = 20^2
Example for family 2: 14400 * 441 = 120^2 * 21^2 = 2520^2
Example for family 3: 28800 * 882 = (2 * 120^2) * (2 * 21^2) = 5040^2
Example for family 4: 5449680 * 869445 = 2176740^2
Example for family 5: 169 * 961 = 13^2 * 31^2 = 403^2
Example for family 6: 528 * 825 = (33 * 4^2) * (33 * 5^2) = 660^2. (End)
MATHEMATICA
Select[ Range[11000], (k = Sqrt[ # * FromDigits @ Reverse @ IntegerDigits[#]]; IntegerQ[k] && k != #) &] (* Jean-François Alcover, Nov 30 2011 *)
sdnQ[n_]:=Module[{c=n*IntegerReverse[n]}, c!=n^2&&IntegerQ[Sqrt[c]]]; Select[ Range[11000], sdnQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 25 2016 *)
PROG
(Haskell)
a070760 n = a070760_list !! (n-1)
a070760_list = [x | x <- [0..], let y = a061205 x,
y /= x ^ 2, a010052 y == 1]
-- Reinhard Zumkeller, Apr 10 2012, Apr 29 2011
CROSSREFS
KEYWORD
nonn,nice,base
AUTHOR
Reinhard Zumkeller, May 15 2002
STATUS
approved